Let S be a set of n moving points in the plane. We present a kinetic and dynamic (randomized) data structure for maintaining the convex hull of S. The structure uses O(n) space, and processes an expected number of O(n~2 β_(s+2)(n) log n) critical events, each in O(log~2 n) expected time, including O(n) insertions, deletions, and changes in the flight plans of the points. Here s is the maximum number of times where any specific triple of points can become collinear, β_S(q) = λ_s(q)/q, and λ_s(q) is the maximum length of Davenport-Schinzel sequences of order s on n symbols. Compared with the previous solution of Basch et al., our structure uses simpler certificates, uses roughly the same resources, and is also dynamic.
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机译:让S成为飞机中的一组n移动点。我们提出了一种用于维持S的凸壳的动态和动态(随机)数据结构。该结构使用O(n)空间,并处理预期的O(n〜2β_(s + 2)(n)log n )关键事件,每个在O(log〜2 n)的预期时间,包括点(n)插入,删除和分数的飞行计划中的变化。这里S是任何特定三联点数可以变为共线的最大次数,β_S(q)=λ_s(q)/ q,λ_s(q)是n符号上的davenport-schinzel序列的最大长度。与之前的Basch等人的解决方案相比。,我们的结构使用更简单的证书,使用大致相同的资源,并且也是动态的。
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